Abstract

Most far-field optical imaging systems rely on lenses and spatially resolved detection to probe distinct locations on the object. We describe and demonstrate a high-speed wide-field approach to imaging that instead measures the complex spatial Fourier transform of the object by detecting its spatially integrated response to dynamic acousto-optically synthesized structured illumination. Tomographic filtered backprojection is applied to reconstruct the object in two or three dimensions. This technique decouples depth of field and working distance from resolution, in contrast to conventional imaging, and can be used to image biological and synthetic structures in fluoresced or scattered light employing coherent or broadband illumination. We discuss the electronically programmable transfer function of the optical system and its implications for imaging dynamic processes. We also explore wide-field fluorescence imaging in scattering media by coherence gating. Finally, we present two-dimensional high-resolution tomographic image reconstructions in both scattered and fluoresced light demonstrating a thousandfold improvement in the depth of field compared to conventional lens-based microscopy.

© 2010 Optical Society of America

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2009 (1)

T. Fessl, S. Ben-Yaish, F. Vacha, F. Adamec, and Z. Zalevsky, “Depth of focus extended microscope configuration for imaging of incorporated groups of molecules, DNA constructs and clusters inside bacterial cells,” Opt. Commun. 282, 2495–2501(2009).
[CrossRef]

2008 (1)

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91(2008).
[CrossRef]

2007 (1)

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nature Phys. 3, 129–134 (2007).
[CrossRef]

2006 (5)

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef] [PubMed]

J. Ryu, S. S. Hong, K. P. Horn, D. F. Freeman, and M. S. Mermelstein, “Multibeam interferometric illumination as the primary source of resolution in optical microscopy,” Appl. Phys. Lett. 88, 171112 (2006).
[CrossRef]

J. R. Fienup, “Lensless coherent imaging by phase retrieval with an illumination pattern constraint,” Opt. Express 14, 498–508 (2006).
[CrossRef] [PubMed]

P. Dufour, M. Piché, Y. De Konnick, and N. McCarthy, “Two-photon excitation fluorescence microscopy with a high depth of field using an axicon,” Appl. Opt. 45, 9246–9252 (2006).
[CrossRef] [PubMed]

M. Boin and A. Haibel, “Compensation of ring artefacts in synchrotron tomographic images,” Opt. Express 14, 12071–12075 (2006).
[CrossRef] [PubMed]

2005 (3)

2004 (2)

A. Grinvald and R. Hildesheim, “VSDI: a new era in functional imaging of cortical dynamics,” Nat. Neurosci. 5, 874–885(2004).
[CrossRef]

S. H. Hong, M. S. Mermelstein, and D. M. Freeman, “Reflective acousto-optic modulation with surface acoustic waves,” Appl. Opt. 43, 2920–2924 (2004).
[CrossRef] [PubMed]

2003 (2)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

C. Dunsby and P. M. W. French, “Techniques for depth-resolved imaging through turbid media including coherence-gated imaging,” J. Phys. D 36, R207–R227 (2003).
[CrossRef]

2002 (2)

J. Sharpe, U. Ahlgren, T. Perry, B. Hill, A. Ross, J. Hecksher-Sorensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296, 541–545 (2002).
[CrossRef] [PubMed]

R. Heintzmann and T. M. Jovin, “Saturated patterned excitation microscopy—a concept for optical resolution improvement,” J. Opt. Soc. Am. A 19, 1599–1609 (2002).
[CrossRef]

2000 (5)

S. Basu and Y. Bresler, “O(N2log2N) filtered backprojection reconstruction algorithm for tomography,” IEEE Trans. Image Process. 9, 1760–1772 (2000).
[CrossRef]

M. G. L. Gustafson, “Surpassing the lateral resolution limit by a factor of two using structured illumination,” J. Microsc. 198, 82–87 (2000).
[CrossRef]

S. M. Mermelstein, D. F. Feldkhun, and L. G. Shirley, “Video-rate surface profiling with acousto-optic accordion fringe interferometry,” Opt. Eng. 39, 106–113 (2000).
[CrossRef]

G. E. Cragg and P. T. C. So, “Lateral resolution enhancement with standing evanescent waves,” Opt. Lett. 25, 46–48 (2000).
[CrossRef]

G. Indebetouw, P. Klysubun, T. Kim, and T. C. Poon, “Imaging properties of scanning holographic microscopy,” J. Opt. Soc. Am. A 17, 380–390 (2000).
[CrossRef]

1999 (2)

1998 (1)

H. Choi and D. C. Munson, Jr., “Direct-Fourier reconstruction in tomography and synthetic aperture radar,” Int. J. Imaging Syst. Technol. 9, 1–13 (1998).
[CrossRef]

1997 (3)

1994 (1)

1991 (2)

L. Sica, “Estimator and signal-to-noise ratio for an integrative synthetic aperture imaging technique,” Appl. Opt. 30, 206–213 (1991).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

1990 (2)

A. E. T. Chiou and P. Yeh, “Scaling and rotation of optical images using a ring cavity,” Appl. Opt. 29, 1584–1586(1990).
[CrossRef] [PubMed]

P. Hobbs and G. S. Kino, “Generalizing the confocal microscope via heterodyne interferometry and digital filtering,” J. Microsc. 160, 245–264 (1990).
[CrossRef]

1987 (1)

N. D. Ustinov, A. V. Anufriev, A. L. Volpov, Y. A. Zimin, and A. Tolmachev, “Active aperture synthesis in observation of objects via distorting media,” Sov. J. Quantum Electron. 17, 108–110 (1987).
[CrossRef]

1986 (1)

D. W. Swift, “Rotation prisms in series,” Opt. Laser Technol. 18, 213–215 (1986).
[CrossRef]

1985 (1)

1983 (1)

D. C. Munson, Jr., J. D. O’Brien, and W. K. Jenkins, “A tomographic formulation of spotlight-mode synthetic aperture radar,” Proc. IEEE 71, 917–925 (1983).
[CrossRef]

1980 (1)

1972 (1)

D. W. Swift, “Image rotation devices—a comparative survey,” Opt. Laser Technol. 4, 175–188 (1972).
[CrossRef]

1969 (1)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
[CrossRef]

1962 (1)

1873 (1)

E. Abbe, “Beiträge zur theorie des mikroskops and der mikroskopischen wahrnehmung,” Arch. Mikrosk. Anat. EntwMech. 9, 413–418 (1873).
[CrossRef]

Abbe, E.

E. Abbe, “Beiträge zur theorie des mikroskops and der mikroskopischen wahrnehmung,” Arch. Mikrosk. Anat. EntwMech. 9, 413–418 (1873).
[CrossRef]

Adamec, F.

T. Fessl, S. Ben-Yaish, F. Vacha, F. Adamec, and Z. Zalevsky, “Depth of focus extended microscope configuration for imaging of incorporated groups of molecules, DNA constructs and clusters inside bacterial cells,” Opt. Commun. 282, 2495–2501(2009).
[CrossRef]

Ahlgren, U.

J. Sharpe, U. Ahlgren, T. Perry, B. Hill, A. Ross, J. Hecksher-Sorensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296, 541–545 (2002).
[CrossRef] [PubMed]

Alexandrov, S. A.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef] [PubMed]

Anufriev, A. V.

N. D. Ustinov, A. V. Anufriev, A. L. Volpov, Y. A. Zimin, and A. Tolmachev, “Active aperture synthesis in observation of objects via distorting media,” Sov. J. Quantum Electron. 17, 108–110 (1987).
[CrossRef]

Baldock, R.

J. Sharpe, U. Ahlgren, T. Perry, B. Hill, A. Ross, J. Hecksher-Sorensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296, 541–545 (2002).
[CrossRef] [PubMed]

Baraniuk, R. G.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91(2008).
[CrossRef]

Barret, H. B.

Basu, S.

S. Basu and Y. Bresler, “O(N2log2N) filtered backprojection reconstruction algorithm for tomography,” IEEE Trans. Image Process. 9, 1760–1772 (2000).
[CrossRef]

Ben-Yaish, S.

T. Fessl, S. Ben-Yaish, F. Vacha, F. Adamec, and Z. Zalevsky, “Depth of focus extended microscope configuration for imaging of incorporated groups of molecules, DNA constructs and clusters inside bacterial cells,” Opt. Commun. 282, 2495–2501(2009).
[CrossRef]

Blahut, R. B.

R. B. Blahut, Theory of Remote Image Formation (Cambridge U. Press, 2004).
[CrossRef]

Bloom, D. M.

D. M. Bloom, “Grating light valve: revolutionizing display technology,” Proc. SPIE 3013, 165–171 (1997).
[CrossRef]

Boin, M.

Boppart, S. A.

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nature Phys. 3, 129–134 (2007).
[CrossRef]

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, 1986).

Bresler, Y.

S. Basu and Y. Bresler, “O(N2log2N) filtered backprojection reconstruction algorithm for tomography,” IEEE Trans. Image Process. 9, 1760–1772 (2000).
[CrossRef]

Carney, P. S.

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nature Phys. 3, 129–134 (2007).
[CrossRef]

Cathey, W. T.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Chiou, A. E. T.

Chiu, M. Y.

Choi, H.

H. Choi and D. C. Munson, Jr., “Direct-Fourier reconstruction in tomography and synthetic aperture radar,” Int. J. Imaging Syst. Technol. 9, 1–13 (1998).
[CrossRef]

Cragg, G. E.

Davenport, M. A.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91(2008).
[CrossRef]

Davidson, D.

J. Sharpe, U. Ahlgren, T. Perry, B. Hill, A. Ross, J. Hecksher-Sorensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296, 541–545 (2002).
[CrossRef] [PubMed]

De Konnick, Y.

Dowski, E. D.

Drexler, W.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

Duarte, M. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91(2008).
[CrossRef]

Dufour, P.

Dunsby, C.

C. Dunsby and P. M. W. French, “Techniques for depth-resolved imaging through turbid media including coherence-gated imaging,” J. Phys. D 36, R207–R227 (2003).
[CrossRef]

Fedlkhun, D. F.

D. F. Fedlkhun, “Fourier domain sensing,” U.S. patent application 20090316141 (2008).

Feldkhun, D.

D. Feldkhun and K. Wagner, “Fourier analysis and synthesis tomography: dynamic measurement of 2D and 3D structure,” in Novel Techniques in Microscopy Conference (Optical Society of America, 2009), paper NWA3.

D. Feldkhun and K. Wagner, “Fourier analysis and synthesis tomography: a structured illumination approach to computational imaging,” in Computational Optical Sensing and Imaging (COSI) Conference (Optical Society of America, 2007).

Feldkhun, D. F.

S. M. Mermelstein, D. F. Feldkhun, and L. G. Shirley, “Video-rate surface profiling with acousto-optic accordion fringe interferometry,” Opt. Eng. 39, 106–113 (2000).
[CrossRef]

Fercher, A. F.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

Fessl, T.

T. Fessl, S. Ben-Yaish, F. Vacha, F. Adamec, and Z. Zalevsky, “Depth of focus extended microscope configuration for imaging of incorporated groups of molecules, DNA constructs and clusters inside bacterial cells,” Opt. Commun. 282, 2495–2501(2009).
[CrossRef]

Fienup, J. R.

Fixler, D.

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Freeman, D. F.

J. Ryu, S. S. Hong, K. P. Horn, D. F. Freeman, and M. S. Mermelstein, “Multibeam interferometric illumination as the primary source of resolution in optical microscopy,” Appl. Phys. Lett. 88, 171112 (2006).
[CrossRef]

Freeman, D. M.

S. H. Hong, M. S. Mermelstein, and D. M. Freeman, “Reflective acousto-optic modulation with surface acoustic waves,” Appl. Opt. 43, 2920–2924 (2004).
[CrossRef] [PubMed]

W. Hemmert, M. S. Mermelstein, and D. M. Freeman, “Nanometer resolution of three-dimensional motions using videointerference microscopy,” in Twelfth IEEE International Conference on Micro Electro Mechanical Systems, 1999. MEMS ’99 (IEEE, 1999), pp. 302–308.
[CrossRef]

French, P. M. W.

C. Dunsby and P. M. W. French, “Techniques for depth-resolved imaging through turbid media including coherence-gated imaging,” J. Phys. D 36, R207–R227 (2003).
[CrossRef]

Fujimoto, J. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

García, J.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Grinvald, A.

A. Grinvald and R. Hildesheim, “VSDI: a new era in functional imaging of cortical dynamics,” Nat. Neurosci. 5, 874–885(2004).
[CrossRef]

Gustafson, M. G. L.

M. G. L. Gustafson, “Surpassing the lateral resolution limit by a factor of two using structured illumination,” J. Microsc. 198, 82–87 (2000).
[CrossRef]

Gustafsson, M. G. L.

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. USA 102, 13081–13086 (2005).
[CrossRef] [PubMed]

Gutzler, T.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef] [PubMed]

Haibel, A.

Hecht, D. L.

D. L. Hecht, “Three dimensional acoustooptics dispersion effects in acoustooptic devices for optical information processing,” in Ultrasonics Symposium (IEEE, 1983), pp. 463–466.

Hecksher-Sorensen, J.

J. Sharpe, U. Ahlgren, T. Perry, B. Hill, A. Ross, J. Hecksher-Sorensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296, 541–545 (2002).
[CrossRef] [PubMed]

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Heintzmann, R.

Hemmert, W.

W. Hemmert, M. S. Mermelstein, and D. M. Freeman, “Nanometer resolution of three-dimensional motions using videointerference microscopy,” in Twelfth IEEE International Conference on Micro Electro Mechanical Systems, 1999. MEMS ’99 (IEEE, 1999), pp. 302–308.
[CrossRef]

Hildesheim, R.

A. Grinvald and R. Hildesheim, “VSDI: a new era in functional imaging of cortical dynamics,” Nat. Neurosci. 5, 874–885(2004).
[CrossRef]

Hill, B.

J. Sharpe, U. Ahlgren, T. Perry, B. Hill, A. Ross, J. Hecksher-Sorensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296, 541–545 (2002).
[CrossRef] [PubMed]

Hillman, T. R.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef] [PubMed]

Hitzenberger, C. K.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

Hobbs, P.

P. Hobbs, “Ultrasensitive laser measurements without tears,” Appl. Opt. 36, 903–920 (1997).
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P. Hobbs and G. S. Kino, “Generalizing the confocal microscope via heterodyne interferometry and digital filtering,” J. Microsc. 160, 245–264 (1990).
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P. Hobbs, Building Electro-Optical Systems: Making It All Work (Wiley, 2000).
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Hong, S. H.

Hong, S. S.

J. Ryu, S. S. Hong, K. P. Horn, D. F. Freeman, and M. S. Mermelstein, “Multibeam interferometric illumination as the primary source of resolution in optical microscopy,” Appl. Phys. Lett. 88, 171112 (2006).
[CrossRef]

Horn, K. P.

J. Ryu, S. S. Hong, K. P. Horn, D. F. Freeman, and M. S. Mermelstein, “Multibeam interferometric illumination as the primary source of resolution in optical microscopy,” Appl. Phys. Lett. 88, 171112 (2006).
[CrossRef]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
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Hutchin, R. A.

R. A. Hutchin, “Microscope for producing high resolution images without precision optics,” U.S. patent 4,584,484 (22 April 1986).

Indebetouw, G.

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D. C. Munson, Jr., J. D. O’Brien, and W. K. Jenkins, “A tomographic formulation of spotlight-mode synthetic aperture radar,” Proc. IEEE 71, 917–925 (1983).
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Jovin, T. M.

Juskaitis, R.

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, 1988).

Kelly, K. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91(2008).
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Kim, T.

Kino, G. S.

P. Hobbs and G. S. Kino, “Generalizing the confocal microscope via heterodyne interferometry and digital filtering,” J. Microsc. 160, 245–264 (1990).
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Klysubun, P.

Laska, J. N.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91(2008).
[CrossRef]

Lasser, T.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

Leith, E. N.

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
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Mandrosov, V. I.

V. I. Mandrosov, “Panoramic microscope with interfering illuminating beams,” Proc. SPIE 3568, 167–177 (1999).
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V. I. Mandrosov, Coherent Fields and Images in Remote Sensing (SPIE Press, 2003).

Marks, D. L.

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nature Phys. 3, 129–134 (2007).
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McCarthy, N.

Mermelstein, M. S.

J. Ryu, S. S. Hong, K. P. Horn, D. F. Freeman, and M. S. Mermelstein, “Multibeam interferometric illumination as the primary source of resolution in optical microscopy,” Appl. Phys. Lett. 88, 171112 (2006).
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S. H. Hong, M. S. Mermelstein, and D. M. Freeman, “Reflective acousto-optic modulation with surface acoustic waves,” Appl. Opt. 43, 2920–2924 (2004).
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W. Hemmert, M. S. Mermelstein, and D. M. Freeman, “Nanometer resolution of three-dimensional motions using videointerference microscopy,” in Twelfth IEEE International Conference on Micro Electro Mechanical Systems, 1999. MEMS ’99 (IEEE, 1999), pp. 302–308.
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M. S. Mermelstein, “Synthetic aperture microscopy,” Ph.D. dissertation (MIT, 1999).

M. S. Mermelstein, “Multiple beam pair optical imaging,” U.S. patent 6,016,196 (18 January 2000).

Mermelstein, S. M.

S. M. Mermelstein, D. F. Feldkhun, and L. G. Shirley, “Video-rate surface profiling with acousto-optic accordion fringe interferometry,” Opt. Eng. 39, 106–113 (2000).
[CrossRef]

Munson, D. C.

H. Choi and D. C. Munson, Jr., “Direct-Fourier reconstruction in tomography and synthetic aperture radar,” Int. J. Imaging Syst. Technol. 9, 1–13 (1998).
[CrossRef]

D. C. Munson, Jr., J. D. O’Brien, and W. K. Jenkins, “A tomographic formulation of spotlight-mode synthetic aperture radar,” Proc. IEEE 71, 917–925 (1983).
[CrossRef]

Neil, M. A. A.

O’Brien, J. D.

D. C. Munson, Jr., J. D. O’Brien, and W. K. Jenkins, “A tomographic formulation of spotlight-mode synthetic aperture radar,” Proc. IEEE 71, 917–925 (1983).
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Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2000).

Oron, D.

Perry, T.

J. Sharpe, U. Ahlgren, T. Perry, B. Hill, A. Ross, J. Hecksher-Sorensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296, 541–545 (2002).
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Piché, M.

Poon, T. C.

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
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Ralston, T. S.

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nature Phys. 3, 129–134 (2007).
[CrossRef]

Ross, A.

J. Sharpe, U. Ahlgren, T. Perry, B. Hill, A. Ross, J. Hecksher-Sorensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296, 541–545 (2002).
[CrossRef] [PubMed]

Ryu, J.

J. Ryu, S. S. Hong, K. P. Horn, D. F. Freeman, and M. S. Mermelstein, “Multibeam interferometric illumination as the primary source of resolution in optical microscopy,” Appl. Phys. Lett. 88, 171112 (2006).
[CrossRef]

J. Ryu, “Resolution improvement in optical microscopy by use of multi-beam interferometric illumination,” Ph.D. dissertation (MIT, 2003).

Sampson, D. D.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef] [PubMed]

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Sharpe, J.

J. Sharpe, U. Ahlgren, T. Perry, B. Hill, A. Ross, J. Hecksher-Sorensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296, 541–545 (2002).
[CrossRef] [PubMed]

Shirley, L. G.

S. M. Mermelstein, D. F. Feldkhun, and L. G. Shirley, “Video-rate surface profiling with acousto-optic accordion fringe interferometry,” Opt. Eng. 39, 106–113 (2000).
[CrossRef]

Sica, L.

Silberberg, Y.

Simpson, R. G.

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, 1988).

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Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
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Streibl, N.

Stroud, R.

J. P. Xu and R. Stroud, Acousto-Optic Devices: Principles, Design, and Applications (Wiley-Interscience, 1992).

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Sun, T.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91(2008).
[CrossRef]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
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D. W. Swift, “Rotation prisms in series,” Opt. Laser Technol. 18, 213–215 (1986).
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D. W. Swift, “Image rotation devices—a comparative survey,” Opt. Laser Technol. 4, 175–188 (1972).
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Takhar, D.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91(2008).
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Tal, E.

Tolmachev, A.

N. D. Ustinov, A. V. Anufriev, A. L. Volpov, Y. A. Zimin, and A. Tolmachev, “Active aperture synthesis in observation of objects via distorting media,” Sov. J. Quantum Electron. 17, 108–110 (1987).
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V. Tuchin, Tissue Optics, 2nd ed. (SPIE, 2007).
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Upatnieks, J.

Ustinov, N. D.

N. D. Ustinov, A. V. Anufriev, A. L. Volpov, Y. A. Zimin, and A. Tolmachev, “Active aperture synthesis in observation of objects via distorting media,” Sov. J. Quantum Electron. 17, 108–110 (1987).
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Vacha, F.

T. Fessl, S. Ben-Yaish, F. Vacha, F. Adamec, and Z. Zalevsky, “Depth of focus extended microscope configuration for imaging of incorporated groups of molecules, DNA constructs and clusters inside bacterial cells,” Opt. Commun. 282, 2495–2501(2009).
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A. VanderLugt, Optical Signal Processing (Wiley-Interscience, 1992).

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N. D. Ustinov, A. V. Anufriev, A. L. Volpov, Y. A. Zimin, and A. Tolmachev, “Active aperture synthesis in observation of objects via distorting media,” Sov. J. Quantum Electron. 17, 108–110 (1987).
[CrossRef]

Wagner, K.

D. Feldkhun and K. Wagner, “Fourier analysis and synthesis tomography: dynamic measurement of 2D and 3D structure,” in Novel Techniques in Microscopy Conference (Optical Society of America, 2009), paper NWA3.

D. Feldkhun and K. Wagner, “Fourier analysis and synthesis tomography: a structured illumination approach to computational imaging,” in Computational Optical Sensing and Imaging (COSI) Conference (Optical Society of America, 2007).

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Wolf, E.

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
[CrossRef]

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J. P. Xu and R. Stroud, Acousto-Optic Devices: Principles, Design, and Applications (Wiley-Interscience, 1992).

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Zalevsky, Z.

T. Fessl, S. Ben-Yaish, F. Vacha, F. Adamec, and Z. Zalevsky, “Depth of focus extended microscope configuration for imaging of incorporated groups of molecules, DNA constructs and clusters inside bacterial cells,” Opt. Commun. 282, 2495–2501(2009).
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N. D. Ustinov, A. V. Anufriev, A. L. Volpov, Y. A. Zimin, and A. Tolmachev, “Active aperture synthesis in observation of objects via distorting media,” Sov. J. Quantum Electron. 17, 108–110 (1987).
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Appl. Opt. (6)

Appl. Phys. Lett. (1)

J. Ryu, S. S. Hong, K. P. Horn, D. F. Freeman, and M. S. Mermelstein, “Multibeam interferometric illumination as the primary source of resolution in optical microscopy,” Appl. Phys. Lett. 88, 171112 (2006).
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IEEE Signal Process. Mag. (1)

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91(2008).
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IEEE Trans. Image Process. (1)

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Int. J. Imaging Syst. Technol. (1)

H. Choi and D. C. Munson, Jr., “Direct-Fourier reconstruction in tomography and synthetic aperture radar,” Int. J. Imaging Syst. Technol. 9, 1–13 (1998).
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J. Microsc. (2)

P. Hobbs and G. S. Kino, “Generalizing the confocal microscope via heterodyne interferometry and digital filtering,” J. Microsc. 160, 245–264 (1990).
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M. G. L. Gustafson, “Surpassing the lateral resolution limit by a factor of two using structured illumination,” J. Microsc. 198, 82–87 (2000).
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J. Opt. Soc. Am. A (3)

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C. Dunsby and P. M. W. French, “Techniques for depth-resolved imaging through turbid media including coherence-gated imaging,” J. Phys. D 36, R207–R227 (2003).
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Nat. Neurosci. (1)

A. Grinvald and R. Hildesheim, “VSDI: a new era in functional imaging of cortical dynamics,” Nat. Neurosci. 5, 874–885(2004).
[CrossRef]

Nature Phys. (1)

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nature Phys. 3, 129–134 (2007).
[CrossRef]

Opt. Commun. (2)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
[CrossRef]

T. Fessl, S. Ben-Yaish, F. Vacha, F. Adamec, and Z. Zalevsky, “Depth of focus extended microscope configuration for imaging of incorporated groups of molecules, DNA constructs and clusters inside bacterial cells,” Opt. Commun. 282, 2495–2501(2009).
[CrossRef]

Opt. Eng. (1)

S. M. Mermelstein, D. F. Feldkhun, and L. G. Shirley, “Video-rate surface profiling with acousto-optic accordion fringe interferometry,” Opt. Eng. 39, 106–113 (2000).
[CrossRef]

Opt. Express (5)

Opt. Laser Technol. (2)

D. W. Swift, “Image rotation devices—a comparative survey,” Opt. Laser Technol. 4, 175–188 (1972).
[CrossRef]

D. W. Swift, “Rotation prisms in series,” Opt. Laser Technol. 18, 213–215 (1986).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef] [PubMed]

Proc. IEEE (1)

D. C. Munson, Jr., J. D. O’Brien, and W. K. Jenkins, “A tomographic formulation of spotlight-mode synthetic aperture radar,” Proc. IEEE 71, 917–925 (1983).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. USA 102, 13081–13086 (2005).
[CrossRef] [PubMed]

Proc. SPIE (2)

V. I. Mandrosov, “Panoramic microscope with interfering illuminating beams,” Proc. SPIE 3568, 167–177 (1999).
[CrossRef]

D. M. Bloom, “Grating light valve: revolutionizing display technology,” Proc. SPIE 3013, 165–171 (1997).
[CrossRef]

Rep. Prog. Phys. (1)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66, 239–303 (2003).
[CrossRef]

Science (2)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

J. Sharpe, U. Ahlgren, T. Perry, B. Hill, A. Ross, J. Hecksher-Sorensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296, 541–545 (2002).
[CrossRef] [PubMed]

Sov. J. Quantum Electron. (1)

N. D. Ustinov, A. V. Anufriev, A. L. Volpov, Y. A. Zimin, and A. Tolmachev, “Active aperture synthesis in observation of objects via distorting media,” Sov. J. Quantum Electron. 17, 108–110 (1987).
[CrossRef]

Other (23)

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H.Gross, ed., Handbook of Optical Systems (Wiley-VCH, 2005), Vol.  2.
[CrossRef]

R. A. Hutchin, “Microscope for producing high resolution images without precision optics,” U.S. patent 4,584,484 (22 April 1986).

M.Harwit, ed., Hadamard Transform Optics (Academic, 1979).

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, 1988).

T. M. Turpin, “Image synthesis using time sequential holography,” U.S. patent 5,751,243 (12 May 1998).

J. Ryu, “Resolution improvement in optical microscopy by use of multi-beam interferometric illumination,” Ph.D. dissertation (MIT, 2003).

M. S. Mermelstein, “Synthetic aperture microscopy,” Ph.D. dissertation (MIT, 1999).

M. S. Mermelstein, “Multiple beam pair optical imaging,” U.S. patent 6,016,196 (18 January 2000).

D. Feldkhun and K. Wagner, “Fourier analysis and synthesis tomography: a structured illumination approach to computational imaging,” in Computational Optical Sensing and Imaging (COSI) Conference (Optical Society of America, 2007).

D. Feldkhun and K. Wagner, “Fourier analysis and synthesis tomography: dynamic measurement of 2D and 3D structure,” in Novel Techniques in Microscopy Conference (Optical Society of America, 2009), paper NWA3.

D. F. Fedlkhun, “Fourier domain sensing,” U.S. patent application 20090316141 (2008).

A. VanderLugt, Optical Signal Processing (Wiley-Interscience, 1992).

J. P. Xu and R. Stroud, Acousto-Optic Devices: Principles, Design, and Applications (Wiley-Interscience, 1992).

D. L. Hecht, “Three dimensional acoustooptics dispersion effects in acoustooptic devices for optical information processing,” in Ultrasonics Symposium (IEEE, 1983), pp. 463–466.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

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[CrossRef]

P. Hobbs, Building Electro-Optical Systems: Making It All Work (Wiley, 2000).
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R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, 1986).

K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2000).

V. Tuchin, Tissue Optics, 2nd ed. (SPIE, 2007).
[CrossRef]

W. Hemmert, M. S. Mermelstein, and D. M. Freeman, “Nanometer resolution of three-dimensional motions using videointerference microscopy,” in Twelfth IEEE International Conference on Micro Electro Mechanical Systems, 1999. MEMS ’99 (IEEE, 1999), pp. 302–308.
[CrossRef]

Supplementary Material (5)

» Media 1: AVI (8077 KB)     
» Media 2: AVI (4057 KB)     
» Media 3: AVI (4071 KB)     
» Media 4: AVI (3165 KB)     
» Media 5: AVI (2091 KB)     

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Figures (10)

Fig. 1
Fig. 1

Three-dimensional OTF support of a spatially incoherent lens-based imaging system representing the range of spatial frequencies captured by the aperture. The aperture acts as a low-pass filter with a cutoff at 2 NA / λ and results in a “missing cone” of spatial frequencies. The DOF varies as λ / NA 2 according to the f z OTF extent.

Fig. 2
Fig. 2

(a) Key optical elements of an acousto-optic DEEP microscope. A two-tone RF drive signal diffracting two first-order beams is illustrated for clarity; however, s ( t ) and the diffracted first-order field can be more complex. (b) A running fringe pattern produces a modulated detector signal, its amplitude and phase corresponding to the complex Fourier coefficient at the spatial frequency of the fringes. Multiple fringe patterns measure a slice through the object’s 3D Fourier space.

Fig. 3
Fig. 3

(a) Reflective implementation of a DEEP microscope. The acousto-optically diffracted first-order beams are rotated using a prism or other means and projected as plane waves onto the sample using a large NA and working-distance optic (coarse phase errors in the optic can be compensated electronically). The sample can be tilted and/or rotated to access different Fourier planes for 3D measurements. The modulated light fluoresced or scattered from the object is collected with high efficiency onto a high-speed detector, whose signal is tomographically processed to reconstruct the object. (b) Key steps in 2D and 3D image synthesis by filtered backprojection. (c) Tilted-plane sampling of Fourier space makes 3D reconstruction possible using a 3D extension of the Fourier slice theorem. (d) A real-space picture of filtered backprojection: A 2D object is decomposed into (time-domain) 1D projections using structured illumination. Each projection is filtered with a ramp filter to compensate for radial sampling and “smeared” along the projection axis. The smeared backprojections are summed to build up a 2D image in real time, projection by projection (Media 1).

Fig. 4
Fig. 4

(a) Time-multiplexed (sequential) sampling. The object is illuminated with one fringe pattern at a time, resulting in a large DOF. Period, amplitude, phase, and orientation of illumination pattern may be chosen independently for each sample (dashed/dotted lines represent past/future samples). Fourier sample resolution is determined by the acousto-optic access time, t a , scaled by the velocity of sound v s and magnification, M, of the illumination optics. (b) FM sampling. The object is illuminated with multiple spatial frequencies to measure multiple samples along a Fourier slice simultaneously, thereby speeding up the measurement. However, the DOF is reduced due to coherent contributions from several redundant tilted interference patterns at each spatial frequency. (c) Nonredundant FM sampling. Since there are no redundant beats in the RF signal, each detected carrier maps to a distinct Fourier sample, however, the samples are not collinear. (d) Double-sided nonredundant FM sampling. Symmetric RF tone pairs produce nonredundant beats, while signal contributions due to redundant tilted interference patterns at other frequencies are rejected (dotted gray impulses, small dots in Fourier space). The remaining samples lie along a Fourier slice resulting in a large DOF at the cost of reduced signal strength. (e) Continuous FM sampling. A continuous RF spectrum can be used to measure an entire Fourier slice with a reduced DOF. As in Fig. 1, the illustrated f x f z OTF section can be found by mapping the RF spectrum onto the k-surface and autocorrelating.

Fig. 5
Fig. 5

(a) The ideal paraxial angular phase front due to the Fresnel propagator, H 0 ( 0 , k y ; z ) , can be linearized in the small region spanned by the spot function, A ( 0 , k y κ ) . (b) Since the pupil phase error function varies much slower than the angular phase front, it can be similarly linearized (the phase errors are greatly exaggerated). (c) The linearized phase functions result in a linear sum of tilted and phase-shifted plane waves under a Gaussian envelope illuminating the object. A slight y shift of the Gaussian envelope due to the linear term of the phase error function is negligible compared to the envelope width.

Fig. 6
Fig. 6

(a) Height and contour maps of the magnitude of the z-dependent 1D OTF of the specified example DEEP system plotted using Eq. (22). The modulation signal driving the Bragg cell has a flat-top RF spectrum spanning 20 MHz . The width of the illustrated sinc profiles, Δ z , limits the DOF at each frequency. The triangular OTF profile at z = 0 is the autocorrelation of the rectangular RF spectrum. Note that Δ z has a minimum at half of the maximum frequency (the mid-frequency), in accordance with Fig. 4e. (b) Halving of the width of the RF spectrum quadruples the DOF measure, Δ z . (c) 1D OTF for an arbitrary asymmetric synthetic pupil function amplitude profile. (d) The width of the main sinc lobe, Δ z , at the mid-frequency is plotted as a function of RF spectral width (assuming a rect spectrum). Δ z is found to vary quadratically with the inverse of the RF bandwidth, corresponding to the quadratic dependence of DOF on the inverse of NA in conventional lens-based imaging systems. (e) 1D OTF for a single-tone RF drive signal. This plot slightly overestimates the DOF since Eq. (22) does not account for y dependence of the OTF several millimeters away from the focal plane.

Fig. 7
Fig. 7

A complex 2D OTF with inversion symmetry can be synthesized by combining multiple 1D OTFs obtained by rotating the illumination with respect to the object. Each 1D OTF may be synthesized as a continuous autocorrelation function or sequentially from discrete Fourier samples. An interpolating ramp filter W 2 D ( k r ) is applied to compensate for radially increasing intersample spacing. For example, in this way, it is possible to synthesize a 2D OTF that is circularly asymmetric and has missing regions as illustrated.

Fig. 8
Fig. 8

(a) White-light interference: an acousto-optic deflector (AOD) illuminated by a dispersion-compensated broadband light source, such as a superluminescent diode, a femtosecond laser, a supercontinuum source, or even an LED, can be used to project moving “white-light” wide-field interference patterns with high contrast and large axial extent. (b) Broadband interference fringes obtained by illuminating a Te O 2 AOD with a strobed “white” LED (Cree XR-E) having an 1 mm 2 emitting area. Because of the common-path grating interferometer configuration, the light source need not be temporally or spatially coherent (given a sufficient AOD acceptance angle). (c) Coherence gating: when a scattering medium is illuminated with a broadband interference pattern, ballistic photons (dotted lines) produce high-contrast fringes at the spatial frequency being measured, whereas various scattering paths (thin lines) contribute an unwanted distribution of spatial frequencies. However, differences in optical paths (e.g., arrowed lines) that exceed the light source coherence length produce only weak intensity modulation at the detector, resulting in improved ballistic signal visibility. Light scattered or fluoresced by the object (wavy lines) in response to the moving fringes can take any path out of the scattering medium and contributes to the signal as long as it is detected. (d)–(f) Simulated beam propagation of interference patterns through a highly scattering medium for monochromatic and broadband light with fractional bandwidths of 0.2 and 1, typical of a femtosecond laser and a supercontinuum source, respectively. In each case, we computed the DEEP detector signal due to a frequency-swept fringe pattern illuminating a grating structure with a period of 6 λ 0 placed at ten different depths in the medium. The field magnitude in the medium is displayed for illumination matching the grating period. The mean transport length (MTL) is shown in white. Also plotted are peak-normalized Fourier slices computed at each grating depth. Coherence gating increases penetration depth of the fringe pattern by a factor of 2–3, depending on the source bandwidth, compared to monochromatic illumination. For the widest bandwidth illumination, the Fourier peak due to the grating structure can be detected three to four MTLs below the surface. (Media 2, Media 3)

Fig. 9
Fig. 9

(a) Key elements of the proof-of-concept DEEP microscope. A double-sided RF chirp applied to the Bragg cell sweeps two first-order diffracted beams, which interfere at the sample. A fast detector measures the sample’s response. A mechanized right-angle prism rotates the illumination. (b) Swept-frequency sampling of the Fourier plane for 25 illumination rotation prism orientations as imaged by a CCD camera. (c) A conventional dark-field image of an Air Force (AF) resolution target using the DEEP objective. (d) Reconstructions of the AF resolution target using filtered backprojection as a function of defocus. The entire Group 7 is resolved throughout the 4 mm axial range, illustrating the large DOF attainable with DEEP microscopy. The circular artifacts in the reconstructions are due to backreflections from uncoated surfaces in the optical system.

Fig. 10
Fig. 10

Conventional images (left) and DEEP reconstructions (right) of fluorescent samples acquired through the same 0.4 NA objective. (a) Autofluorescence in the legs of a bug. Leg sections separated by 180 μm are in focus simultaneously in the DEEP image. (b) A 1.9 mm deep field of 2.27 μm Nile Red fluorescent beads dispersed in glycerin jelly. All beads within the volume are in focus simultaneously in the reconstruction. Distortions in the images of beads located near the DOF limits are due to precession of the rotating prism and can be corrected in postprocessing, as the insets show. The precession-corrected bead images demonstrate resolution below 2 μm . A faster but lower-quality measurement, as well as a sequence of bead images at 20 μm depth intervals taken through a monitoring eyepiece, are available for comparison (Media 4, Media 5).

Equations (26)

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i d ( t ) I obj ( x , y ) [ 1 + m 2 cos ( 2 π ( f 0 u u ν o t ) ) ] d x d y [ I obj ( f x , f y ) e j 2 π ( f x x + f y y ) d f x d f y ] × [ 1 + m 2 e j 2 π ( f 0 u u ν 0 t ) + c.c. ] d x d y I obj ( 0 , 0 ) + m 2 I obj ( f 0 x , f 0 y ) e j 2 π ν 0 t + c.c.
U + 1 ( x , y , t ) a ( x , y ) s a ( t + y v o ) e j ω + t + c.c. ,
s a ( t + y v o ) h a ( t ) s m ( t ) δ ( t t a 2 + M y v a ) .
U o ( x , y , z , t ) = U + 1 ( x , y , t ) * * p i ( x , y ) * * h 0 ( x , y ; z ) ,
F x y { U o ( x , y , z , t ) } [ A ( k x , k y ) * S a ( k y v o ) e j k y v o t ] × P i ( k x , k y ) H 0 ( k x , k y ; z ) e j ω + t + c.c. = e j ω + t A ( k x , k y κ ) [ e j k 0 z e j ( k x 2 + k y 2 ) z / 2 k 0 ] × P i ( k x , k y ) S a ( κ v o ) e j κ v o t d κ + c.c.
U o ( x , y , z , t ) e j k 0 z e j ω + t e j κ ( y v o t κ z / 2 k 0 ) a ( x , y κ z k 0 ) × [ e j κ Δ ϕ k y ( 0 , κ ) P i ( 0 , κ ) S a ( κ v o ) ] d κ + c.c.
i ˜ d ( t ) I obj ( x , y , z ) | e j κ ( y κ z / 2 k 0 ) × a ( x , y κ z k 0 ) P S ( κ v o ) e j κ v o t d κ | 2 d x d y d z ,
F { i ˜ d ( t ) } d x d y d z I obj ( x , y , z ) e ( x 2 + y 2 ) / r o 2 e j Ω m y / v o × R Ω m { e ( j 2 z / r o 2 k 0 ) Ω m 2 z / 2 k 0 v o 2 e 2 Ω m z y / r o 2 k 0 v o P S ( Ω m ) } ,
P S ( Ω m ) = e j Δ ϕ k y ( 0 , Ω m / v o ) Ω m / v o × P i ( 0 , Ω m v o ) S m ( Ω m ) H a ( Ω m ) e j Ω m t a / 2 ,
P S ( Ω m ; Ω m ) = P S ( Ω m ) δ ( Ω m Ω m ) + P S ( Ω m ) δ ( Ω m + Ω m ) ,
F { i ˜ d ( t ) } I obj ( x , y , z ) e ( x 2 + y 2 ) / r o 2 × e 2 ( Ω m z / r o k 0 v o ) 2 d x d z e j Ω m y / v o d y [ P S ( Ω m ) P S * ( Ω m ) δ ( Ω m + 2 Ω m ) + P S * ( Ω m ) P S ( Ω m ) δ ( Ω m 2 Ω m ) ] .
F { i ˜ d ( t ) } = i ˜ d ( t ) e j Ω m t d t i ˜ d ( y v o ) e j k y y d y = F y { i ˜ d ( y v o ) } ,
F y { i ˜ d ( y v o ) } F y { P y { I obj ( x , y , z ) [ e ( x 2 + y 2 ) / r o 2 × e 2 ( Ω m z / r o k 0 v o ) 2 ] } } R ˜ Ω m { P S ( Ω m ; Ω m ) } ,
F y { P y { I ( x , y , z ) } } SF k y { I ( x , y , z ) } ,
F y { i ˜ d ( y / v o ) } = SF k y { I obj ( x , y , z ) w ( x , y , z , Ω m ) } H 1 D ( Ω m ; Ω m ) ,
H 1 D ( Ω m ; Ω m ) = R ˜ Ω m { P S ( Ω m ; Ω m ) } = P S ( Ω m ) P S * ( Ω m ) δ ( Ω m + 2 Ω m ) + P S * ( Ω m ) P S ( Ω m ) δ ( Ω m 2 Ω m ) .
r z = r o v o 2 λ 0 ν m ,
H 1 D ( Ω m ) SF k y { I im ( x , y , z ) } SF k y { I obj ( x , y , z ) w ( x , y ) } = i = 0 N R ˜ Ω m { P S ( Ω m ; Ω i ) } ,
z r o v o 2 λ 0 ν m .
F y { i ˜ d ( y / v o ) } F y { P y z { I obj ( x , y , z ) [ e ( x 2 + y 2 ) / r o 2 ] } } × R Ω m { e ( j 2 z / r o 2 k 0 ) Ω m 2 z / 2 k 0 v o 2 P S ( Ω m ) } d z .
F y { i ˜ d ( y / v o ) } F y { P y z { I im ( x , y ; z ) } } d z = SF k y ; z { I obj ( x , y ; z ) w ( x , y ) } H 1 D ( Ω m ; z ) d z ,
H 1 D ( Ω m ; z ) = SF k y ; z { I im ( x , y ; z ) } SF k y ; z { I obj ( x , y ; z ) w ( x , y ) } = R Ω m { e ( j 2 z / r o 2 k 0 ) Ω m 2 z / 2 k 0 v o 2 P S ( Ω m ) } .
H 2 D ( k r ; z ) = W 2 D ( k r ) n = 0 N 1 H 1 D ( k r v 0 ; z ; θ = n π N ) ,
F x y { I im ( x , y ; z ) } d z = H 2 D ( k r ; z ) F x y { I obj ( x , y ; z ) } d z ,
H 3 D ( k ρ ) = W 3 D ( k ρ ) n = 0 N 1 H 1 D ( k ρ v 0 ; θ = n π N ; ϕ = m π M ) ,
F x y z { I im ( x , y , z ) } = H 3 D ( k ρ ) F x y z { I obj ( x , y , z ) } .

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